where subscripts in covariance matrices remind us that the covariance functions in different layers can be different. The hidden output \({\bf H}\)  is a data matrix consisting of vector-valued hidden functions \({\bf h}({\bf x}_{1:N})\) , entering as input to second GP. In Bayesian inference, the marginalization of the hidden random variables \({\bf h}\)  is not tractable, which leads to various approximation schemes including variational inference [1]}, [2]}, [3]}, [4]}, [5]} and expectation propagation [6]}.
